Question: $f(x) = -x^{2}+1$ What is the range of $f(x)$ ?
Answer: Consider the range of $-x^{2}$ The range of $x^2$ is $\{\, y \mid y \ge 0 \,\}$ Multiplying by $-1$ flips the range to $\{\, y \mid y \le 0 \,\}$ To get $-x^{2}+1$, we add $1$.